Statistics, data and evidence · Perspectives

Can a single average represent a group fairly?

Means, medians and percentages compress many people into one number. That makes comparison possible, but it can hide differences that matter. This question asks when summarising helps knowledge and when it distorts it.

Claims

Averages make patterns visible that are impossible to see in raw data, and choosing the right average for the purpose gives fair knowledge.
Statistics can show its own limits, for example by reporting spread and subgroup figures alongside averages.

Counterclaims

The same data can support opposite conclusions depending on how it is grouped, so summaries can mislead even when correctly calculated.
Choosing which average to report can be a political decision, as in debates over mean versus median income.

Real-life situations from mathematics

Berkeley admissions, 1973

Overall figures for graduate admissions at the University of California, Berkeley, appeared to show women admitted at a lower rate than men. A 1975 analysis by Bickel and colleagues showed that within most departments women did as well or better; women had applied more often to departments that admitted fewer applicants. This is an example of Simpson's paradox.

Mean and median income

In countries with a few very high earners, mean income is well above median income, so the 'average' person earns less than the average. Which figure is quoted changes the story.

Check dates and figures in a reliable source before you use them, and cite that source.

Use this in your TOK work

Essay. Fits titles about simplification, representation or the human sciences.

Exhibition. A school report showing a class average could make a personal object for a prompt about whether knowledge can be objective.

Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.

Themes and study heading

Knowledge and politics Perspectives

Different views of what mathematics is and whose it is.